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Let R be a rectangle that is the union of a finite number of rectangles R_i, 1 \leq i \leq n, satisfying the following conditions:

(i) The sides of every rectangle R_i are parallel to the sides of R.
(ii) The interiors of any two different rectangles R_i are disjoint.
(iii) Each rectangle R_i has at least one side of integral length.

Prove that R has at least one side of integral length.

Variant: Same problem but with rectangular parallelepipeds having at least one integral side.

Slični zadaci

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